Question

write the equation of the line that is parallel to the line y=-5/3x-2 and goes throught the point (-3,1)

Answer 1

y = (-5/3)x - 4

Step-by-step explanation:

The equation of a line with slope m that goes through the point (x1, y1) is:

`y-y_1=m(x-x_1)_{}`

Additionally, two lines are parallel if they have the same slope.

The slope of the line y = (-5/3)x - 2 is (-5/3) because it is the number beside x.

So, the slope of our line is also -5/3.

Therefore, replacing m by -5/3 and (x1, y1) by (-3, 1), we get that the equation of the line is:

`\begin{gathered} y-1=-(5)/(3)(x-(-3)) \\ y-1=-(5)/(3)(x+3) \end{gathered}`

Finally, solving for y, we get:

`\begin{gathered} y-1=-(5)/(3)x-((5)/(3)\cdot3) \\ y-1=-(5)/(3)x-5 \\ y=-(5)/(3)x-5+1 \\ y=-(5)/(3)x-4 \end{gathered}`

So, the answer is:

y = (-5/3)x - 4